Conventional analog circuits often incorporate voltage and/or current references. Examples of such analog circuits include resistor-capacitor (RC) oscillators and phase-locked loop (PLL) circuits. A bandgap voltage reference is a voltage reference circuit that is widely used in integrated circuits as a temperature-independent and process-independent voltage reference. A constant current reference, I, can be obtained using a bandgap voltage, Vbg, and a stable resistance R. The relationship between the current reference, I, the bandgap voltage, Vbg, and the resistance, R, is represented by I=Vbg/R.
A constant current reference is difficult to obtain in practice because of temperature and process variations that can affect the resistance R. For example, if a MOS resistor having resistance R is operated in an environment that is subject to varying temperature, then the resistance R can change when the temperature changes, resulting in a varying (i.e., non-constant) current reference. Similarly, variations in semiconductor manufacturing processes can yield resistors having varying resistances. For example, the resistances of poly-resistors produced by a stable manufacturing process can vary by around ±30%. Therefore, a current reference which is generated based on a resistance value R can vary with process and temperature variations.
One conventional solution for reducing resistor variation is to use a highly accurate external resistor (external to the integrated circuit chip). However, highly accurate external resistors are expensive and consume valuable layout area.